There are a number of posts that address this issue, as well as issues raised by responses to this post. I posted somewhere "no true Scotsman"--I'm not claiming my post was enlightening in itself, but the post I was responded to (and the entire thread) was, IMO, enlightening.
As for averaging, yes, you can: if a nudge is ineffective, then its result will be random, and a bunch of ineffective nudges will average zero effectiveness. The effective nudges will then push the overall average above zero. We don't see that. (The same would be true for medical interventions, unless some cause harm.)
As for being able to try lots of them: in some circumstances, maybe. But when a government is trying to nudge people towards some desired behavior (vaccination, say, to take a random example), they don't try sending out a bunch to different groups of people, then polling each of those groups to see which groups--and therefore which nudges--moved. And it's not always practical, anyway (and the vaccination example is a case where it's almost certainly not practical).
> if a nudge is ineffective, then its result will be random
Ineffective and random are different. Ineffective means that the effect size is smaller than required.
For example, if you read "Paracetamol was ineffective for pain relief after surgery" it doesn't necessarily mean that the effect of paracetamol is unpredictable, inconsistent, immeasurable, or that it had no effect or negative effect. You would most likely interpret it to mean that the paracetamol did have an effect but it was insufficient - the patient was still in too much pain.
Similarly, if a nudge intervention was ineffective, it doesn't tell you how it failed, only that it didn't reach the threshold for success. And it certainly doesn't tell you anything about how well an aggregate of some effective and some ineffective results would perform.
As for averaging, yes, you can: if a nudge is ineffective, then its result will be random, and a bunch of ineffective nudges will average zero effectiveness. The effective nudges will then push the overall average above zero. We don't see that. (The same would be true for medical interventions, unless some cause harm.)
As for being able to try lots of them: in some circumstances, maybe. But when a government is trying to nudge people towards some desired behavior (vaccination, say, to take a random example), they don't try sending out a bunch to different groups of people, then polling each of those groups to see which groups--and therefore which nudges--moved. And it's not always practical, anyway (and the vaccination example is a case where it's almost certainly not practical).
See also threads that mention A/B testing.